I just started a multivariable calculus class, and I have a few problems I could use some help with.
I will provide my work so that you people know what I'm thinking.
1.) The monthly payments, P dollars, on a mortgage in which A dollars were borrowed at an annual interest rate of r% for t years is given by . Is f an increasing or decreasing function of A? Of r? Of t?
Is this question asking if A, r, and t are plotted separately against P, would the graph be increasing or decreasing?
If so, I got:
for A : Increasing
for r : Increasing
for t : Decreasing
2.)Describe the set of points whose distance from the x-axis equals the distance from the yz-plane.
I don't know exactly how to word this one. I think if I would draw the xyz coordinate axes, and label the origin O, then the answer would be the line exactly bisecting the angle XOY. Is this correct? (if anyone can understand what i'm saying)
3.)Find the equations of planes that just touch the sphere and are parallel to:
(a) the xy-plane
(b) the yz-plane
(c) the xz-plane
(a) Since it has to be parallel to the xy-plane, we just deal with the z-coordinate.. so we have to subtract/add the radius to the z-coordinate of the center of the sphere in order to get the plane to just touch the sphere. So I think this would be z = 7 and z =-1.
(b) x = 6 and x = -2 (by the same reasoning)
(c) y = 7 and y = -1 (by the same reasoning)
I'm not sure if all of this is correct or not (it might be). I just need some reassurance since this is my first time working in 3-dimensions, and I find the transition a little confusing.